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A304654
a(n) = (n!)^2 * Sum_{k=1..n-1} 1/(k^2*(n-k)).
2
0, 0, 4, 27, 328, 6500, 192216, 7952112, 438941952, 31185057024, 2772643115520, 301622403456000, 39413353102848000, 6091955683706880000, 1099401414283210752000, 229088914497045356544000, 54589580461769879715840000, 14750581694440372638842880000
OFFSET
0,3
FORMULA
Recurrence: (2*n - 3)*a(n) = (6*n^3 - 25*n^2 + 33*n - 12)*a(n-1) - (n-2)^2*(6*n^3 - 29*n^2 + 42*n - 15)*a(n-2) + (n-3)^3*(n-2)^3*(2*n - 1)*a(n-3).
a(n)/(n!)^2 ~ Pi^2/(6*n).
MATHEMATICA
Table[(n!)^2 * Sum[1/(k^2*(n-k)), {k, 1, n-1}], {n, 0, 20}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, May 16 2018
STATUS
approved